The \( \mu \) -reversibility of the associated unlabeled diffusion was left open in [1]}.
Combining [2]} and [1]}, we find that the unlabeled process given by the solution of Eq. (REF ) obtained in [1]} is reversible with respect to \( \mu _\beta \)  for \( \beta = 1, 4\) .
For a general \( \beta > 0 \) , we expect that the reversible probability measure of the unlabeled diffusion given by the solution to ISDE (REF ) is the sine\(_{\beta } \)  random point field.
This remains an open problem, except for \( \beta = 1,2,4 \)  [5]}.
